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Pertanyaan

Bunga majemuk dirumuskan dengan M subscript n equals M open parentheses 1 plus b close parentheses to the power of n. Nyatakanlah n dalam M subscript nM dan b.

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

rumus n yang dinyatakan dalam M subscript nM dan b adalah n equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator log space open parentheses begin display style M subscript n over M end style close parentheses over denominator log space open parentheses 1 plus b close parentheses end fraction end cell end table.

Pembahasan

Ingat kembali sifat bentuk logaritma berikut ini.

  • log presuperscript a space open parentheses b over c close parentheses equals log presuperscript a space b minus log presuperscript a space c 
  • log presuperscript a space b c equals log presuperscript a space b plus log presuperscript a space c 
  • log presuperscript a space open parentheses b to the power of m close parentheses equals m space open parentheses log presuperscript a space b close parentheses 

Dengan sifat  bentuk logaritma di atas, didapat perhitungan berikut ini.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell M subscript n end cell equals cell M open parentheses 1 plus b close parentheses to the power of n end cell row cell log space M subscript n end cell equals cell log space M open parentheses 1 plus b close parentheses to the power of n end cell row cell log space M subscript n end cell equals cell log space M plus log space open parentheses 1 plus b close parentheses to the power of n end cell row cell log space M subscript n minus log space M end cell equals cell log space M plus n space log space open parentheses 1 plus b close parentheses minus log space M end cell row cell fraction numerator log space M subscript n minus log space M over denominator log space open parentheses 1 plus b close parentheses end fraction end cell equals cell fraction numerator n space log space open parentheses 1 plus b close parentheses over denominator log space open parentheses 1 plus b close parentheses end fraction end cell row cell fraction numerator log space M subscript n minus log space M over denominator log space open parentheses 1 plus b close parentheses end fraction end cell equals n row cell fraction numerator log space open parentheses begin display style M subscript n over M end style close parentheses over denominator log space open parentheses 1 plus b close parentheses end fraction end cell equals n end table end style   

Jadi, rumus n yang dinyatakan dalam M subscript nM dan b adalah n equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator log space open parentheses begin display style M subscript n over M end style close parentheses over denominator log space open parentheses 1 plus b close parentheses end fraction end cell end table.

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